# Less than or Equal to

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Main article: Comparison function
 `≤`

Less than or Equal to (`≤`) is a comparison function which tests whether the left argument is tolerantly less than or equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the negation of Less than (`<`), and in fact was called Not greater in APL\360.

## Boolean function

When the arguments to Less than or Equal to are Boolean, it is the material implication Boolean function, also known as the IMPLY gate:

`≤` `0` `1`
`0` `1` `1`
`1` `0` `1`

In the context of logic, it can be read as implies.

Less than or Equal to Scan is an occasionally used pattern related to Less than Scan. While `<\` changes all 1s after the first to 0, `≤\` changes all 0s after the first to 1. Thus `≤\A` ${\displaystyle \Leftrightarrow }$ `~<\~A`.

```      ≤\ 1 0 1 0 0 0 1 0
1 0 1 1 1 1 1 1
```

`≤\` appears in the FinnAPL idiom library as entry 350, "Not first zero".